Generation of shaped surfaces



March 1963 e. o. RAWSTRON ETAL 3,

GENERATION OF SHAPED SURFACES Filed Feb. 16, 1960 3 Sheets-Sheet 1 Fl F2 2 [ACL- Inventors 6v 0. Ha ws from H. 5 Reason By W Attorneys March 5, 1963 G. o. RAWSTRON ETAL 3,079,731

GENERATION 0F SHAPED SURFACES Filed Feb. 16, 1960 s Sheets-Sheet 2 lnveniors G 0. Ra ws iron 1?. 6'. Reason A ttorn e ys March 5, 1963 e. o. RAWSTRON ETAL 3,079,731

GENERATION OF SHAPED SURFACES 3 Sheets-Sheet 3 Filed Feb. 16, 1960 F/G8. Q Q

Inventors 0. 0. 93 ws {PM 1?. 5 Reason Attorneys United States This invention relates to apparatus for producing on a workpiece a surface of revolution which deviates from a basic surface by relatively small amounts at different radial distances from the axis of symmetry. Although not limited thereto, the invention is more especially intended for the generation of what are sometimes known as figured surfaces on optical elements, for such surfaces have hitherto been formed by first producing a rough approximation to the desired surface, for example by moulding or by a lapping process, and then finishing the surface by a laborious figuring process which calls for highly expert skill and involves repeat-ed optical testing between hand rubbing operations until the desired surface has been formed with a sufiicient degree of accuracy. The basic surface may be a plane surface, and in such case the invention is suitable, for example, for the production of the opticalcorrecting plates known as Schmidt plates. Alternatively, the basic surface may be a spherical surface, and there arev many known instances in the optical objective art in which use is made of aspheric lens surfaces which deviate by only small amounts from a basic spherical surface.

The present invention has for its object to provide a simple and efficient apparatus for generating such surfaces whereby the surface is initially formed with so high a degree of accuracy as to render unnecessary the expert figuring process hitherto required.

In the apparatus according to the present invention, the workpiece is roatated about its axis of symmetry, and interrelated relative movements between the workpiece and the tool are effected in two coordinate directions respectively parallel to and at right angles to a fixed reference axis, which coincides with the axis of symmetry in at cordance with the deviations of the desired surface from such basic surface.

The basic surface may consist of a plane surface at right angles to the axis of symmetry, and in such case, preferably, a relative traversing movement between the workpiece and the tool is effected in a direction at right angles to the axis of symmetry, and a relative correcting movement controlled in accordance with the deviations of the desired surface from the basic plane surface at the various radial distances from the axis of symmetry is effected in a direction parallel to the axis of symmetry.

Alternatively, the basic surface may consist of a spherical surface centered on the axis of symmetry, and in such case, preferably, a relative movement controlled in accordance with the shape of the basic surface is superimposed on a relative correcting movement controlled in accordance with the deviations from the basic surface to determine the relationship between the coordinate relative movements. Conveniently, the control in accordance with the shape of the basic spherical surface is effected by relatively guiding the two coordinae movements along a circular path. The relative correcting movement in accordance with the deviations from the basic spherical surface may be effected in a direction parallel to the fixed reference axis, whereby the superimposed relative movements are interrelated in accordance with a system of combined polar and rectangular coordinates generated by rectangular coordinate relative movements.

The relative correcting movement is preferably controlled by a cam device shaped in accordance with the deviations of the desired surface from the basic surface, whether such basic surface be plane or spherical. Preferably, the shape of the cam device is determined in accordance with a chosen large multiple of the deviations, and the correcting movement is derived therefrom through a transmission mechanism having a reduction ratio dependent on such chosen multiple, means being provided for effecting relative movement between the cam device and the transmission mechanism in accordance with the relative traversing movement.

Whilst other forms of cam device may be used, it is preferred to employ an optical cam device comprising a sheet bearing a curved line which contrasts in respect of light-transmitting properties with the background constituted by the adjacent portions of the sheet, the relative correcting movement being derived from relative movement between such cam device and an optical unit for following the curved line on the sheet. Such optical unit may act to direct a small beam of light through the optical cam device on to photoelectric means sensitive to lateral displacement between the beam of light and the curved line on the sheet, electrical means being provided operative in accordance with the output of the photoelectric means to effect relative movement between the optical unit and the cam device for correcting such lateral displacement. The relative movement between the cam device and the optical unit is preferably effected by a reversible electric motor whose direction of rotation is controlled by the photoelectric means, whereby such relative movement consists of small oscillations from one side to the other of the correct relative position determined by the cam device.

The invention may be carried into practice in various ways, but some convenient alternative practical arrangements according thereto for accurately generating'a surface o-f revolution deviating by relatively small amounts from a basic plane or spherical surface, for example the surface of a lens'or other optical element, are illustrated somewhat diagrammatically in the accompanying drawings, in which FIGURE 1 is a plan view of one arrangement in which the basic surface is a plane surface,

FIGURE 2 is a front view of the arrangement of FIG- URE 1,

FIGURE 3 is a sectional view of the workh'older use in the arrangement of FIGURES 1 and 2,

FIGURES 4 and 5 are partial plan and front views illustrating apparatus for generating a cam device, for use in an alternative arrangement,

FIGURE 6 illustrates in plan view the alternative arrangement employing the cam device of FIGURES 4 and 5, i

FIGURE 7 is a front view of the arrangement of FIG- URE 6,

FIGURE 8 is a sectional view on the line 88 of FIGURE 6,

FIGURE 9 is a diagram of an electric circuit used in the arrangement of FIGURES 6-8,

FIGURE 10 is a fragmentary view illustrating the form of cam device used in the arrangement of FIGURES 6-8, and

FIGURE 11 illustrates a modified arrangement for use when the basic surface consists of a spherical surface.

In the arrangement of FIGURES 1 and 2, in which the basic surface is a plane surface at right angles to the axis of symmetry of the desired surface, which may for instance be the surface of a correcting plate of the Schmidt type, the workholder consists of a fitting A on the end new 3 of an accurate spindle A journalled horizontally in a housing A secured to a fixed base B, the spindle being driven through suitable coupling meansA}. by an electric inotor A ThespindleA is so. mounted infits housing as ,to be substantially wholly. devoid of anyshaKein its rot-ation,; for example in one orother of theways described, in United StatesPatent No. 2,791,170. It is likewise imfportan-t to ensure that the workpiece C is accurately centered: on the axis of the spindleAK In the case of a Schmidt plate, the .workpiece C will usually consist of a fcirculardisc of glass carried in a cell. To ensure accuracy or mounting-on the spindle, the cell C is provided (as shown. in FIGURE. 3) with accurately ground. locating .faces C ;which cooperate with complementary faces A provided on theend of the spindle A the cell. being sccured on a loose screwthread C so .as to clamp such faces inengagement. The cell C likewise has accurate seating faces C for recciving-the-glass disc C which'will usually be held against such faces by wax in recesses C The toolholderD is secured to a cross slide E which can slide. for example on three bearing balls E on guide tracks F on acarriage F, which-in turn can slide similarly on balls F on guide tracks B on a fixed base slab B ;The two sets oi guide'tracks F and B lie accurately ag r htian gsone another, those on the base slab B being accurately parallel to the axis of the horizontal spindle=A ca-rryingthe workholder A. The carriage F ismoved along its-guide tracks B by a lever, G through a connecting rod G having trounded ends abutting re- ;spectivelyagainst the-lever G and against a projection F tromthe carriage F havingamicrometer fitting F for fine adjustment of the-axial position of the carriage relatively tothe lever,v a; spring G being; provided between the lever andthe carriage to hold the parts in engagement. The lever G is driven atits other end in accordance wi th the deviations of the desired surface from the'basic plane surface under the control of a cam device carried by a horizontal table H mounted on .a verticalspindle H driven through worm gearing H by .another electric motor This spindle H carries aerankarm H to -which one endof .a connectingrod] is adjustably connected, the other end of such connecting rod being em- .ployedto drive the cross-slide E on its guide tracks F acrossthecarriage A,microrneter fitting.J is pro- ,.vided for adjusting the effective length ol:' the connecting rod J. In order to avoid errors in the drive'of the crossslide E duetovarying inclination of the connectingflrod I, this rod is nbt connected directly to the crossfslide, but

'to a bar I which extends parallel to' theaxisofthe horizontal s pindle'A and engages between two pairs of roll- :ers E? on thecross-slide E, the bar]? being constrained against longitudinal movementgby means of a roller-J engaging in a'fixedslot B extending at right angles to v the direction of the horizontal spindle axis. 1

The cam device may be arranged in ,vanousways, but ,in one simple form consists of a flexible steel strip K clamped at alarge number of; close1y spaced points, such as K K along its length to the horizontal table These clamps K are spaced approximately round an arc of a circle centered on the vertical spindle H1 andcan be accuratel-y adjusted radially With-respect thereto to give the desired can't shape. These adjustments are made in accordance with calculated measurements defining the deviations of, the'desi red surface from the basic plane surface.- ..When, asWill usually be the case with a ,Schmidt plate, these deviations are very small, the actual cam shape is preferably determined in accordance-with a chosenlarge multiple of the deviations, for example two hundred timesthe calculated deviations, the lever G being arrangedlto give a 200:1 reduction ratio, to provide the a correct deviations in the actual movement of the carriage Thelever pivot G is preferably adjustableto enable the reduction ratioto be varied, as. may be; convenient.

For the purpose of setting the camK. in accordance with the calculatedmeascrements of the deviations, the crossslide E carries a microscope L for viewihg'a'pair of c accurately divided movable [glass scales L L one of which L extends transversely to the axis of the horizontal spindle A and the other L parallel thereto. These scales L L each move at right angles to -their lengthsand are guided in their movements by means of projectionsL L sprin -pressedagainst the accurately polished edges of a rectangular glass reference plate L secured tothe base. The transverse scale L is moved in the axial direction by means of a projection E? on the cross-slideEcarryinga pair of rollers E between which a rod L carried by the s:ale L engages. The axial scale L is similarly moved in the transverse direction by means of a pair of rollers E on the cross-slide E between which arod L'l carried by the scaleL engages. The microscope L is sejpnsttioned as to be sighted on the point of intersection orgnre two scales L L and it will be clear that it will remain sighted thereon inv allpositions of the cross-slide E, as the scales move relatively to one another. I

The transverse scale L is finelydivided into. equally spacedgraduations appropriate to the radial positions at which the measurements of the deviations of the desired surface from the axis of symmetry. are calculated, the zero point of the stale being 'so'positioned .thatwhen it is in the centre of the field of the microscope L, the cross} slide E. is in the correct position for the .tool D to. .b'e accurately aligned on theho'rizontal -spindle axis.. The axial scale L is similarly graduated and inQorder to. get highly accurate sub-divisions of the scale divisions, the microscope L is provided with an adjustable Vernier graticule.

mm, for setting inseam Kin accord'a'n'e with the calculatedv measurements for an individual Schmidt plate,

the connecting rod lfondrivingthe cross slide E is first adjusted alongthe crank arm H 'on the vertical spindleH to give a'suitable'relationship between the angular rotation ofthe horizontal table H and the transverse movements ofthe cross-slide E for an adequate length of cam in relation to the maximum radius of the desired Schmidt plate,

.the total angular, movement of the crankar'mfi over the WhoIelength ofcam K being not greater than about 120. degrees, with. the beginning and end. positions, more or less equally'spaced on eithersid'e of a radial; line from ,the vertical spindle axis parallel to the horizontal 'sp indle ,axis. .The length of 'theconnecting rod J is correspon'd- ,inglyadjust'ed to give the desiredi' r'elationship between Ith'ejzero points. of the transverse 'scaleL and of the crank arm H The leverratio is also chosen to suit the magnitude of the, deviation calculationgthe lever pivot (3 being suitably adjusted. s I

The cam striptK is now, clamped in position on the horizontal Qtable Hstarting with the. zero point, thetable being rotated and with it the cross-slidegE moved step by step'in accordance with theg'raduatio'nson the transverse fjscale L viewed through the microscopeflLthe cam clamps K K lheing adjust'ed one by one to the correct positionsj to, suit the chosen multiple of the. deviations, as determined by the calculated deviation mea'sutements on the axial scale L viewed through the microscope L p with the 'aidof the vernier graticule, the movements of the carriage F corresponding to such measurements being transmitted to the cam Kthrough the lever G to deter- L mine the cam positionsfor clamping. \When the camx has been, accurately. clamped in its correct, position throjughouathetool D is insertedinthe toolholder Din its correct position. and the cross-slide. Elis moved so that rthetooltlies just ofi the edge of'thelworkpiece disc C,the

micrometer fitting F on the projection F from the car riageF being adju'sted to move; the tool D axially tothe position ,cor'responding to the desired depth of cut on the dlsg; Whilst a sharply pointed diamond tdol is usually preferable, itrnay be practicable some instance s to emplo y a driven diamond wheel,-preferably using the relatively sharp edgethereof The apparatus is now ready for the actual g er iera tion of the Schmidt plate surface on the disc C, and the two electric motors A H are started up respectively to drive the horizontal spindle A and to traverse the cross-slide E at the appropriate speed across the disc C from the edge to the centre. As this traversing proceeds, the lever G, which engages with the cam K in a substantially radial direction relatively to the vertical spindle H is moved by the cam K so as to transmit to the carriage F the correct deviations, thereby ensuring accurate generation of the desired surface on the dis: C.

This arrangement may be modified by dispensing with the axial scale L altogether and providing a micrometer to measure directly the chosen multiple of the calculated deviation measurements for setting the cam K in position, the micrometer measurements being effected in a radial direction with respect to the vertical spindle H in the position in which the end of the lever G engages with the cam K. Such modification will be described below with reference to FIGURES 4 and 5.

In the foregoing arrangement the cam device is in the form of a thin flexible steel strip K, but it is usually preferable in practice to employ an optical cam device consisting of a dark or opaque line on a translucent sheet or a translucent line on a dark or opaque sheet in conjunction with an optical follower unit. It is especially convenient to employ the arrangement forming the subject of the present applicants copending United States patent application Serial No. 857,816, now abandoned, wherein such line is made up of a series of small dots at equal intervals, in the positions defined by the calculated measurements, the dots preferably being of such a size in relation to the interva's between dots that they overlap one another and form a continuous line, the actual cam line consisting of the line of centres of the dots.

projection being provided with an arcuate slot H (for a purpose to be described below) over which the plate M rests. The plate is provided with two accurately ground surfaces M M on one of its longer edges and a third ground surface M on one of its end edges, these three ground surfaces M M M engaging with three locating pins M M M on the projection H from the table H, whereby it can be positioned with accuracy thereon. Clamps M are provided to hold the plate M in'the position determined by the locating pins.

A photographic unit N, comprising a small aperture N within a closed casing N which also houses a source of light N a condensing lens N for concentrating the I light on the aperture N and an objective N for focussing the aperture N on the photographic plate M. is movably mounted so that the vertical optical axis of the beam of light passing through the aperture N can move in a substantially radial direction with respect to the vertical axis of the horizontal table H. Since, however, its total movement is quite small, it will sufiice for it to be mounted on the end of a long pivoted arm N The movements of the unit N are controlled by a micrometer head N whereby such movements can be effected with a high degree of accuracy in accordance with calculated measurements. A shutter N is provided in the casing of the photographic unit N, so as normally to shut off the light from the aperture N this shutter being operated, for example by a press button N on the casing, to permit the light to pass from the aperture N when desired.

This device is operated in a manner generally analogous to that above described for the setting of the steel strip cam K. Thus the table H bearing the photographic plate M is rotated step by step through a number of closely spaced positions accurately determined by observing the graduations on the transverse scale L through the microscope L. In each position, the micrometer head N is operated in accordance with the appropriate calculated measurement, and when the photographic unit N has thus been positioned the shutter N is opened to expose the small circular portion of the sensitive photographic plate M on which the light from the aperture N is focussed, thus recording one of the desired round dots on the plate. It should be mentioned that an opaque screen (not shown) is provided to minimise risk of fogging the sensitive plate M by the light used for viewing the scale L and setting the micrometer head N the plate M itself being slow in order still further to minimise the risk of fogging.

When all the dots have been recorded, the sensitive plate M is removed and developed, to produce a photographic negative on which a curved line of dark or opaque round dots M (FIGURE 10) appears on a translucent background, such line of dots being shaped in accordance with the calculated deviations of the desired Schmidt plate surface from the basic plane surface. Such photographic negative M is preferably itself used to constitute the optical cam device, but it will be cear that, if it is preferred to use a cam device with translucent dots on a dark or opaque background, the negative may be photographically printed on to another precisely s milar plate (likew se prov ded with the three ground portions on its edges) to form a photographic positive, which can be used as the optical cam device. The plate (whether negative or positive) is then replaced in position on the projection H from the horizontal table H against the locating pins M M M so that it will occupy exactly the same position as before. The photographic unit N is now removed from the long pivoted arm N to be rep aced by the optical follower unit, which cooperates with the optical cam device in practical use.

Such optical follower unit 0 (see FIGURES 6, 7 and 8) also includes a small circular aperture 0 a source of light 0 and a lens system 0 for directing a vertical concentrated beam of light from the source 0 through the aperture 0 If the photographic negative is used as the cam device, this aperture 0 is made larger than that N used during photographing, for example having twice the diameter thereof. Although the source of li ht 0 and the lens system 0 may be mounted vertically above the aperture 0 it is found more convenient, for

reasons of compactness, for the light and lens system to have a horizontal axis, a small mirror 0 inclined at 45 degrees to such axis being provided to deflect the beam vertically down through the aperture 0 The follower unit 0 also includes a beam-splitting device 0 lying vertically beneath the aperture 0 with the optical cam device M between them, the arcuate slot H in the projection H from the horizontal table H thus serving to permit the beam of light through the aperture 0 to pass through the optical cam device to the beam-splitting device 0 which acts to deflect two parts of the beam respectively on to two photoelectric cells 0 0 also carried by the follower unit 0. The operative beamsplitting plane of the beam-splitting device 0 extends tangentially with respect to the vertical axis of the horizontal table H. Whilst the beam-splitting device 0 may consist of an ordinary beam-sp itting prism with its operative edge tangential with respect to such vertical axis, so that the two partial beams to the two photocells pass radially, inwards and onwards, with respect to such axis, it is found more convenient to use a different form of beam-splitting device, which will deflect the two partial beams in opposite directions parallel to the beam-splitting plane. This consists (as shown in FIGURE 8) of two similar reflecting prisms side by side with their inclined reflecting surfaces facing in opposite directions,

. tion.

and O in two'of its arms.

steal theprisfnsides in contact with one another lying in the beam-splitting plane.

The followerunit O is mounted on the long pivoted larmN which previously carried the photographic unit N,'care being. taken to. ensure that its small aperture 0 follows the same substantially radial path with respect to the vertical axis of the horizontal table H as the apertureN of the photographic unit N. The followerf unit vO is'connected to'the'lever G, which operates the tool- .holder D, through a connecting link G having ball ends engaging in recesses in the follower unit 0 and in the lever G, a spring G being provided to maintain the parts in engagement. 7

The two photocells O 0' are connected in a suitable electrical circuit (which may for instance take the form described inlthe specification of the copendin'g application" Serial No. 857,816,, now abandoned, abovernentioned) to control the. operation of a reversible electric the firstO the motor P' is driven in .theopposite direc- This motor P drives a worm P engaging with 'a worm wheel P on'arod P which is in screwthreaded [engagement with a fixed bracket P so that the rodP .will move longitudinally in one direction or the other in accordance with the direction of rotation of'the motor connected thereto.

Thus, when the horiZontal table H is rotated to drive .the optical cam, device slowly past the'small aperture 'motor P, the arrangement being 'such that when the out- I put-of the first photocell O exceeds'that of the second ,O' 'the motor P is driven in one direction, whilst when ;the output of the secondphotocell O7 exceeds that of P. The roundedjend of this rod engages either with the .follower unit O itself or'(as shown) withthe lever G O of the follower unit 0, the beam of light through the aperture will pass through a small circular patch of the .cam device, across themiddle of which the line of dots M passes. The light passing through the portion of 'such circular patch on one'side of the line'of dotsM passes to, one; photocell O 'and that through the portion on the other side of the line of dots passes to the other photocell 0 If the line of "dots M 'is not exactly central in the small circular patch, more light will pass to .one photocell than to, the other, with the result that the electric, motor P will be caused torotate so as to move ,the followerunit O in the direction to equalise the two portions of the. circular patch on the two sides of the line .of dots M The follower unit 0 will in fact move past the position of equality, asthe result of which the outputs of the .two photocells O 0' will be caused to differ in the opposite sense and'will thereby cause the motor .1 to be reversed, thus bringing the follower unit 0 back again.

The follower unit will therefore be caused to oscillate backwards and forwards from one side to the other of its correct position. as determined by the line of dots M. I These oscillations can be made very small with .:suitable design of the electric circuit, but they will ensure highlysensitive following of the curve of the line of dots, and therefore highly accuratejcontrol of the 1 movement of'the tool D for the generation of the desired surface. I V p r V A preferred form for such electric circuit is described in the specification'of the copending application Serial 'No. 857,817 above mentioned, buta simplified form of such circuit is shown byway of example in FlGURE '9. This circuit includes an electronic valve Q, thepotential of the grid Q of which is controlled by a circuit resembing a bridge circuit, having the 'two photocells A n I The other two 'arms contain resistances Q Q and a further resistance Q is connected across the diagonal of the bridge. The arrangement is such that, when the photocell outputs are balanced, suficient anode current'flows to close a sensitive relay Q in'the anode circuit of the valve Q. A shunt circuit'is connected across the relay Q containing an auxiliary bias supply Q and a variable resistance 8 p .i Q", for bringing th e relay into a critical operating pendition by passing a current in opposition to the anode current of the valve. The contacts of the relay Q which open and close in response to variations in t he anode current of the valve Q, control the energisation and deenergisation of a contactor Q controlling reversing contacts Q? in the energising circuit of the reversib'e motor P. In this way, highly sensitive control of direction of rotation of the motor P by the outputs of the 'photocells O O is ensured, thus causing the f ollower unit 0 to follow the line of dots M witha high degree of accuracy as the traversing proceeds, and thereby in turn causing highly accurate generation of the desired surface on the workpiece C. I r a n It should be mentioned that for satisfactory beamsplitting action, the cam line M should not: become too steeply inclinde to the operative beam-splitting plane,

and it is found that the angle between the cam line and .suchiplane' should, not be greater than aboutjq degrees.

In practice, however, this does not present serious difiiculty, for ajreduced inclination can be used if the lever reduction ratio is reduced. When generating the carn device, therefore, the operator should in general choose as large a reduction ratio (within the available range) as is possible without involving an excessive inclination of the cam line to the beam-splitting plane. A v H 7 If it is desired to use the photo graphic positive, instead of the negative, for the'optical cam device, the apertuife 0 in the optical follower unit should preferably be made of the same size as that used in photographing, and the .follower unit should also be providedwith a graticule having a fairly thick straight line marking in the path of the light between the aperture 0 and the beamsplittingdevice 0 such straight line lying in the beamsplitting plane. Thus, as each of the translucent dots of the cam device comes in its turn beneath the aperture O any lateral displacement relatively to the beam-splitting plane will be revealed by the difierent amounts 'Of light passing on the two sides of the graticule line respectively to the two photocells O O I ,7 7 I, It should be noted that such straight line graticule will operate satisfactorily for splitting the beam, even if the spacing between consecutive dots in the line is such that thedotsdo not overlap one another. This makes it practicable, if desired, to manufacture an opticalicarn device by punching small holes through an opaque sheet in the appropriate accu rately'rneasured positionspwithout unduly weakening the sheet by overlapping consecutive holes and thus producing a continuouscam slot. ln a similar Way, the straight line graticule can be used with a row of dark or opaque dots on atransulcent background, when such dots do not overlap one another.

Again, it is not essential to use round dots tomakc up the cam line of the optical cam device, and patches of other shape can be employed, if desired, by the use of an aperture other than circular in the photographic. unit N. Round dots, however, are usually preferable, since their use will permit satisfactory operation over a greatproduce a resultant equivalent to a rotation about'a pivot axis at a radius equal to that 'of the basic spherical surface.

This can readily'be achieved by modifying theforegoing arrangements (as shown in FIGURE 11) to provide an arcua'te'guide R on the cross-slide E of radiusequal to that of the basic spherical surface, such guide cooperating with an abutment to which the correcting movement derived from the lever G is applied. Thus, the projection from the carriage F against which the connecting rod abutting against the lever cooperates in the foregoing arrangements, is removed and replaced by a member R sliding in a ball guide R accurately parallel to the axis of the horizontal spindle A and terminating in a roller R engaging with the arcuate guide R provided on the cross-slide E, the micrometer fitting used for adjustment of the depth of cut still being provided at R on this sliding member R The effect of this modification is that the movement of the carriage F is no longer confined to the correcting movement derived through the lever G from the cam device, but now consists of two superimposed movements, one of which is constituted by such correcting movement while the other is a component movement which cooperates with the movement of the cross-slide E on the carriage to produce the desired resultant rotational traversing movement centered about a vertical axis, which intersects the axis of the horizontal sp'ndle A and may be termed the pivot axis although no actual. pivot is provided.

The arcuate guide R is detachably mounted on the cross-slide'E, so that it can be replaced by another arcuate guide of different radius, when required, and since it is important to ensure that the guide is centered with a high degree of accuracy on a straight line through the tool D parallel to the horizontal spindle axis, it is desirable to provide the mounting for the guide R on the cross-slide E with fine adjustmentmeans (not shown) for tilting the guide to bring its centre into correct alignv ment with such straight line.

When crossed scales L L are used, the accuracy of accordance with calculated measurements.

In order to check the accuracy of mounting of the arcuate guide R, when the transverse scale L alone is used in conjunction with a micrometer head N at the low magnification end of the lever G, a spherical lens having a surface accurately corresponding to the basic spherical surface is first mounted in a cell on the end of the horizontal spindle A (care being taken to clean the lens seatings in the cell thoroughly to avoid positional errors due to dirt), and a precision gauge is fitted into the toolholder D in place of the tool D with its movable gauging element projecting into engagement with the spherical surface. The cross-slide E is then moved, so that the arcuate guide R slides past the abutment roller R with corresponding axial movement of the carriage F, until the gauging element engages with a marginal point of the spherical surface. With the crossslide E held stationary in this position, the horizontal spindle A is rotated at a slow speed, and the gauge readings are watched during this movement. If, as may be the case, for example because of dirt not properly I removed from the cell seatings or due to any untru'th in the edging of the lens, the spherical lens has a slight tilt in its mounting, so that its centre is not quite accurately aligned on the spindle axis, this will be revealed by the gauge readings which will vary from a maximum to a minimum and back again during one complete revolution. The position of maximum error is noted and the spindle A is rotated through exactly a right angle from such position. This will bring the points of maximum and minimum error vertically above and below the spindle axis, so that the horizontal section of the lens surface through the axis is substantially accurately circular. The spindle A is now locked in this position, and the cross-slide E is now operated, so that the gauging element is traversed along this circular section of the surface. The gauge readings during such traverse will indicate whether the arcuate guide R is accurately centered on the spindle axis, the necessary adjustment of the arcuate guide being made to correct any error, so that the gauge readings will remain constant (to the degree of accuracy required) during the traverse. The gauge is now removed from the toolholder D and the tool D inserted therein, the tool being adjusted in its holder to the position in which it just tou:hes the spherical surface. The tool is locked in the toolholder in this position of adjustment, and the spherical lens is removed from the horizontal spindle.

The parts are now ready for setting the cam device, Whether in the form of a steel strip or of an optical cam device, in the manner above described, in accordance with the chosen multiple of the deviations of the desired aspheric surface from the basic spherical surface. When the cam device has been set and the lever pivot G adjusted to suit the chosen ratio, the glass block C on which the aspheric surface is to be generated is mounted in its cell in position on the horizontal spindle, care being taken to remove any dirt from the cell seatings to ensure accurate positioning of the glass block thereon. The cross-slide E is operated to bring the tool D just off the edge of the glass block C, and the micrometer fitting R between the lever G and the abutment R engaging with the arcuate guide R is operated to move the carriage F axially to the position corresponding to the desired depth of cut on the block. The two ecctric motors A and H are now started up and the desired aspheric surface is generated on the workpiece in a manner analogous to that above described.

It should be mentioned that, since the correcting movement in accordance with the deviations is applied in a direction parallel to the horizontal spinde axis, in all relative positions of the tool and workpiece, the relative traversing and correcting movements operate ona system of combined polar and rectangular coordinates, and of course the deviations must also have been calculated on this basis. The fact that deviations calcula'ed on this basis were applied to the cam device on a truly polar coordinate basis is immaterial, since the lever G is operated by the cam device in the radial direction and therefore receives the deviation movements from the cam device on the same basis as they were applied to the cam device.

In the foregoing arrangements, the workholder A has been stationary, except for its rotation about its own axis, and both the traversing movement (whether translational when the basic surface is plane or efiectively rotational when the basic surface is spherical) and the correcting movement in accordance with the deviations, have been applied to the toolholder D, such arrangements operating in the case of a plane basic surface on a rectangular system of coordinates and in the case of a spherical basic surface on a combined polar and rectangular system of coordinates. It will be appreciated, however, that various inversions of such movements'can be used instead, if desired.

Thus, for example, the correcting movement could be applied to the workholder A, by mounting the support for the horizontal spindle A on an axially moving carriage, whilst the traversing movement remains applied to the toolholder D, the toolholder still being mounted on the cross-slide E on the carriage when the basic surface is spherical (a fixed abutment being provided for the arcuate guide R), or being mounted on a simple transverse carriage when the basic surface is plane.

Or again, the traversing movement and the correcting movement could both be applied to the workholder A, by mounting the support for the horizontal spindle A on the cross-slide E on the carriage F, the toolholder D being fixed in position on the base.

In another variant, the traversing movement is applied to the workholder A and the correcting movement to the toolholder D. In the case of a plane basic surface, this is effected by mounting the toolholder D on an axially moving carriage and the support for the horizontal semi-s1 for the arcuate guide R), Whilst the toolholder D is mounted on another axially moving carriage.

v Again, in the case of a spherical basic surface, it is also possible to split up'the two coordinate components of the traversing movement and appl'y one to the workholder 'A and the other to the'toolholder D. be achieved, forexample, by mounting the support for the accurate spindle A on an axially moving'carriage, such carriage also carrying the'arcuate guide'R withwhich cooperates an abutment fixed to a transversely moving car- 'riage,such latter carriage carrying an axially moving crosscam device-and" hotoelect-ric means res onsi'veto'lateral slide which is moved by the lever G in accordance with the correcting movement and carries the toolholder 'D.

v The various alternativearrangements can also be modified in' other wayswithin the scope of the invention. For

' example, it is not es'sential'to the invention for the hori- Zontal table'H, which carries the ca'm'device, to rotate about a pivot axis, and' such table could, if desired, perform 2. straight-line"translational movement, appropriate- -ly"interrelated to 'the relative traversing movement be 12 transmission means has a redu cti'o'nr'atiodependentch such chosen multiple. v l

5. Apparatus as'clairned in claim"4,'in which the'cain deviceconsis'ts of an optical cam device'compri'sin'g a sheetbearitg a curved'line which contrasts in respect of light-transmittingproperties.wd-th the background constituted bythe -adjacent portions of the sheet, and the transmission means includes 'an optical unit cooperating with the cam'device and follower mean's'for c'ausi.. g the This can optical unit to follow the curved line on'the sheet during the relative traversing movement.

6. Apparatus as claimed in claim 5, in which the optical hnit'includesfa source of light, means for directing'a srnall'lieam of light from the source through the opti a1 displacement between the bcam'of light 'and the cur d "line on the sheet, and the followermeans compriss'a reversible electric 'm'oton electrical circuit means forcontrolling thedireetion ofrotatio'n otsuchniotor'in acco d- 'o 'ance with the output of the photoelectric means, "and means whereby the electric motorcauses' relative movement' between the optical cam dev iceand the optical unit for correcting the said lateral displacement, such relative movement consistin'gof small oscillations tram one" side m eioolD anathe workpi ce C. In s h a i 3 :to the other" of the'c'orrect relative" position determined from the basic'surfac'e. The step-by-ste'p movement of 'iflijragfiv the tableduring-generation of the carn'dev'ice would of course take-place along'exactly the same path as its sub- 'sequent movement during manufacture of the desired surface.

bythe'optical cam device. 7 I H '7. Apparatus as claimed in claim 1, whereinfth e has'ic 'surface consists of a spherical surface centered on the 'xisof symmetry, and in whiohthe me'ans for applying i sing mov merit incln'desguidingm s for inte'r 'r elating the'two' component rcc tafigular' cbordinate relative tnu leising'rnc ivem'ents'- toprodu'ce 'a resultant relative traversing movement equivalent to fa rotation about apiv'ot axis intersctingtheaxis' fsymmetry at What we claim as our invention and desire to secure right angles at "a" radius equal to that of'the'basic spher'ical "by Letters Patent is:

1. Apparatus for producing on a workpiece by means 'of'a tool a surface of revolution which deviates from'a basic surface by relatively small amounts at difierent 8. Apparatnsas claimedinclaim7, inwhich the means for superimposing the rel-ative'correoting movement on the relative traversing "movement comprises an'o'ptical radial distances from the 'axis'of symmetry, said appara- 4 device consisting of sheet bearing gurved lif 'tus comprising a fixed base, a workholder for carrying the workpiece, means for-rotating the workholder about an axis constituting the said axis of symmetry, a toolholder for-carrying the tool in operative relationship to the which "contrasts in respect of light-transmitting prop- "erties with the background constituting the adjacent portions of the sheet an'dlis shaped in"accordancewith'the deviations of the desired surface from the basic spherical Workplace on the wmkholder mounting means on "surface,an'optical unit'cooperating with the optical cam base for locatingthe workholder' and toolholder relatively to a fixed reference axis which coincides with the axis of rotation'of the workholder in at least one position thereof, superimposed slideways for confining component reladevice, means for efie'cting relative movement between the optical unit and the optical cam device in'accordan'ce with the relative traversing movement between the workholder and the toolholder, follower means acting during twe movements Between the Workholdfir and the tool such relative movement to cause the optical unit and the holder'to two'coordin'ate directions respectively parallel to and:at right angles to the fixed reference axis, means for applying to "the w'orkholder and the'toolholder a resultant relative traversing movement in accordance with the "shape of: the basic surfac'eunder thecontrol of such slideways, and means for superimposing on such traversing movement a, relative correcting movement in the'direc- ,tion of the; fixed reference, axis in accordance with the deviations-of the desired surface from such basic surface.

2. Apparatus as claimed in claim 1, wherein the basic optical cam device to perform relative working movemets transverse to such relative movement-whereby the optical unit is caused to follow the curved line on the sheet, and transmission means through which the said relative working movements are caused 'to'control the -relative correcting'movement betweenthe workholder and the 'toolholderl v 9. Apparatus as claimed in claim 8, in which the'shape of the cam device is determined in-accordance*with' a chosen large multiple of the said deviations,'and'the transmission means has a reduction ratio' dependent on "such chosen multiple.

10. Apparatus as claimed in claim 8, in which the optical unit comprises a source of light. means for direct- Apparatus as claimed in claim including a cam ing a small beam of light from the source through the device shaped in accordance with the deviations of the desired surface from the basic plane surface, transmission means through Qwhich thecam device controls the relativecorrecting' movement, and means for effecting relative movement between the cam device and the transmission means in accordance with therelative traversing movement between the workholder and the toolholder.

4 Apparatus as claimedin claim 3, in which the shape of the cam device is determined in accordancewith a optical cam device, andphotoelectric'means'responsive to lateral displacement between the bea'm'of light and the curved lineon the sheet for givingan' output for-the "con'trol 'of the follower means.

IL'Apparatus as claimed in claim 10, in which the follower mea s com prises a reversible electric motor, electrical circuit means for con-trolling the directionof rotation of such motor in accordance with the outputof the photoelectric means, and means whereby the electric chosen large multiple of the said deviations, and-the motor acts to cause-the-relativeworking-movements hei3 tween the optical unit and the optical cam device, such relative working movements consisting of small oscillations from one side to the other of the correct position determined by the optical cam device.

12. Apparatus as claimed in claim 7, in which the guiding means comprises two cooperating guide members consisting respectively of an arcuate guide shaped to suit the shape of the basic spherical surface and an abutment cooperating with such arcuate guide, means for mounting one of such two cooperating guide members on the superimposed slideways, and means whereby the correcting movement is applied to the other of such cooperating guide members and is thereby superimposed on the relative traversing movement.

13. Apparatus as claimed in claim 12, in which the means for superimposing the relative correcting movement on the relative traversing movement comprises a cam device shaped in accordance with the deviations of the desired surface from the basic spherical surface, an element cooperating with such cam device, means for effecting relative movement between the cam device and such element in accordance with the relative traversing movement between the workholder and the toolholder whereby the said element is caused to perform working movements transverse to such relative movement dependent on the shape of the cam device, and transmission means through which the working movements of the said element are transmitted to the one of the two said cooperating guide members to which the correcting movement is applied.

14. Apparatus as claimed in claim 13, in which the shape of the cam device is determined in accordance with a chosen large multiple of the said deviations, and the transmission means has a reduction ratio dependent on such chosen multiple.

References Qited in the file of this patent UNITED STATES PATENTS 1,485,258 Dzus Feb. 26, 1924 2,725,776 Hopkins Dec. 6, 1955 2,733,519 Darogo Feb. 7, 1956 

1. APPARATUS FOR PRODUCING ON A WORKPIECE BY MEANS OF A TOOL A SURFACE OF REVOLUTION WHICH DEVIATES FROM A BASIC SURFACE BY RELATIVELY SMALL AMOUNTS AT DIFFERENT RADIAL DISTANCES FROM THE AXIS OF SYMMETRY, SAID APPARATUS COMPRISING A FIXED BASE, A WORKHOLDER FOR CARRYING THE WORKPIECE, MEANS FOR ROTATING THE WORKHOLDER ABOUT AN AXIS CONSTITUTING THE SAID AXIS OF SYMMETRY, A TOOLHOLDER FOR CARRYING THE TOOL IN OPERATIVE RELATIONSHIP TO THE WORKPIECE ON THE WORKHOLDER, MOUNTING MEANS ON THE BASE FOR LOCATING THE WORKHOLDER AND TOOLHOLDER RELATIVELY TO A FIXED REFERENCE AXIS WHICH COINCIDES WITH THE AXIS OF ROTATION OF THE WORKHOLDER IN AT LEAST ONE POSITION THERE- 